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Translation of a sphere towards a rigid plane in an Oldroyd-B fluid

Physical Review Fluids 2024年第8期9卷 083303页

作者： Tachin Ruangkriengsin Rodolfo Brandão Bimalendu Mahapatra Evgeniy Boyko Howard A. Stone Program in Applied and Computational Mathematics Department of Mechanical and Aerospace Engineering Faculty of Mechanical Engineering

We analyze the low-Reynolds-number translation of a sphere towards or away from a rigid plane in an Oldroyd-B fluid under two scenarios: prescribing the sphere's translational velocity, and prescribing the force on the sphere. Leveraging the lubrication approximation and a perturbation expansion in powers of the Deborah number, we develop a comprehensive theoretical analysis that yields analytical approximations for velocity fields, pressures, and forces acting on the sphere. Our framework aids in understanding temporal microstructural changes as the particle-wall gap evolves over time. In particular, we show that alterations in the polymer conformation tensor in response to geometric changes induce additional forces on the sphere. For cases with prescribed velocity, we present a theoretical approach for calculating resistive forces at any order in the Deborah number and utilize a reciprocal theorem to obtain higher-order corrections based on velocity fields in the previous orders. When the sphere translates with a constant velocity, the fluid viscoelasticity decreases the resistive force at the first order. However, at the second-order correction, the direction of the sphere's movement determines whether viscoelasticity increases or decreases the resistive force. For cases with prescribed force, we show that understanding the influence of viscoelasticity on the sphere's translational velocity necessitates a more intricate analysis even at low Deborah numbers. Specifically, we introduce an ansatz for constant force scenarios, and we derive solution forms for general prescribed forces using the method of multiple scales. We find that when a sphere undergoes sedimentation due to its own weight, the fluid viscoelasticity results in a slower settling process, reducing the leading-order sedimentation rate.

关键词： Complex fluids Low Reynolds number flows Lubrication theory Polymer conformation changes Rheology

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A Flow Artist for High-Dimensional Cellular Data 33

A Flow Artist for High-Dimensional Cellular Data

引用

33rd IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2023

作者： MacDonald, Kincaid Bhaskar, Dhananjay Thampakkul, Guy Nguyen, Nhi Zhang, Joia Perlmutter, Michael Adelstein, Ian Krishnaswamy, Smita Yale University Department of Mathematics United States Pomona College Department of Mathematics United States University of Washington Department of Statistics United States Boise State University Department of Mathematics United States Yale University Department of Computer Science United States Yale University Applied Mathematics Program United States Yale University Computational Biology and Bioinformatics Program United States

ISBN: (纸本)9798350324112

We consider the problem of embedding point cloud data sampled from an underlying manifold with an associated flow or velocity. Such data arises in many contexts where static snapshots of dynamic entities are measured, including in high-throughput biology such as single-cell transcriptomics. Existing embedding techniques either do not utilize velocity information or embed the coordinates and velocities independently, i.e., they either impose velocities on top of an existing point embedding or embed points within a prescribed vector field. Here we present FlowArtist, a neural network that embeds points while jointly learning a vector field around the points. The combination allows FlowArtist to better separate and visualize velocity-informed structures. Our results, on toy datasets and single-cell RNA velocity data, illustrate the value of utilizing coordinate and velocity information in tandem for embedding and visualizing high-dimensional data. © 2023 IEEE.

关键词： RNA

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Trustworthy Actionable Perturbations 41

Trustworthy Actionable Perturbations

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41st International Conference on Machine Learning, ICML 2024

作者： Friedbaum, Jesse Adiga, Sudarshan Tandon, Ravi Program in Applied Mathematics University of Arizona TucsonAZ United States Department of Electrical and Computer Engineering University of Arizona TucsonAZ United States

Counterfactuals, or modified inputs that lead to a different outcome, are an important tool for understanding the logic used by machine learning classifiers and how to change an undesirable classification. Even if a counterfactual changes a classifier's decision, however, it may not affect the true underlying class probabilities, i.e. the counterfactual may act like an adversarial attack and "fool" the classifier. We propose a new framework for creating modified inputs that change the true underlying probabilities in a beneficial way which we call Trustworthy Actionable Perturbations (TAP). This includes a novel verification procedure to ensure that TAP change the true class probabilities instead of acting adversarially. Our framework also includes new cost, reward, and goal definitions that are better suited to effectuating change in the real world. We present PAC-learnability results for our verification procedure and theoretically analyze our new method for measuring reward. We also develop a methodology for creating TAP and compare our results to those achieved by previous counterfactual methods. Copyright 2024 by the author(s)

关键词： Adversarial machine learning

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Comparative Analysis of Radial Basis Functions and Cubic Splines for Data Imputation 10

Comparative Analysis of Radial Basis Functions and Cubic Spl...

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10th International Conference on Fuzzy Systems and Data Mining, FSDM 2024

作者： Kitchainukoon, Wisut Sangsuwan, Amornrat Pongchalee, Pornthip Chanthawara, Krittidej Department of Mathematics Faculty of Science and Technology Loei Rajabhat University Loei42000 Thailand Department of Mathematics Faculty of Education Loei Rajabhat University Loei42000 Thailand Department of Applied Mathematics and Statistics Faculty of Science and Liberal Arts Rajamangala University of Technology Isan Nakhon Ratchasima30000 Thailand Program of Mathematics Faculty of Science Ubon Ratchathani Rajabhat University Ubon Ratchathani34000 Thailand

ISBN: (纸本)9781643685694

This study evaluates the effectiveness of Radial Basis Function (RBF) approaches, specifically Gaussian and Multiquadric RBFs, compared to Cubic and Adaptive Splines for data imputation in time-series datasets. Three datasets-multiseasonal, non-stationary, and spikes and drops-were used, with varying data corruption levels to simulate real-world scenarios. Imputation performance was assessed using Root Mean Square Error (RMSE). The results indicate that spline-based methods, particularly Cubic and Adaptive Splines, consistently deliver lower RMSE values, showcasing superior robustness to data variability and high corruption levels compared to RBF methods. This comparative analysis offers insights into selecting appropriate techniques for effective data imputation in time-series analysis. © 2024 The Authors.

关键词： Splines

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Our Role in Solving Global Challenges: An Opinion

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JOURNAL OF THE AMERICAN CHEMICAL SOCIETY 2024年第31期146卷 21193-21195页

作者： Carter, Emily A. Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics and the Andlinger Center for Energy and the Environment Princeton University Princeton New Jersey 08544-5263 United States Princeton Plasma Physics Laboratory Princeton New Jersey 08540-6655 United States

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Space-Time Diffusion Bridge

arXiv

引用

arXiv 2024年

作者： Behjoo, Hamidreza Chertkov, Michael Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ85721 United States

In this study, we introduce a novel method for generating new synthetic samples that are independent and identically distributed (i.i.d.) from high-dimensional real-valued probability distributions, as defined implicitly by a set of Ground Truth (GT) samples. Central to our method is the integration of space-time mixing strategies that extend across temporal and spatial dimensions. Our methodology is underpinned by three interrelated stochastic processes designed to enable optimal transport from an easily tractable initial probability distribution to the target distribution represented by the GT samples: (a) linear processes incorporating space-time mixing that yield Gaussian conditional probability densities, (b) their diffusion bridge analogs that are conditioned to the initial and final state vectors, and (c) nonlinear stochastic processes refined through score-matching techniques. The crux of our training regime involves fine-tuning the nonlinear model, and potentially the linear models – to align closely with the GT data. We validate the efficacy of our space-time diffusion approach with numerical experiments, laying the groundwork for more extensive future theory and experiments to fully authenticate the method, particularly providing a more efficient (possibly simulation-free) inference. © 2024, CC BY.

关键词： Stochastic systems

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Harmonic Path Integral Diffusion

arXiv

引用

arXiv 2024年

作者： Behjoo, Hamidreza Chertkov, Michael Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ85721 United States

Harmonic Path Integral Diffusion (H-PID) introduces a novel approach to sampling from complex, continuous probability distributions by creating a time-dependent "bridge" from an initial point to the target distribution. Formulated as a Stochastic Optimal Control problem, H-PID balances control effort and accuracy through a unique three-level integrable structure: Top Level: Potential, force, and gauge terms combine to form a linearly solvable Path Integral Control system based on Green functions. Mid Level: With quadratic potentials and affine force/gauge terms, the Green functions reduce to Gaussian forms, mirroring quantum harmonic oscillators in imaginary time. Bottom Level: For a uniform quadratic case, the optimal drift/control reduces to a convolution of the target distribution with a Gaussian kernel, enabling efficient sampling. Implementation-wise the low-level H-PID operates without neural networks, allowing it to run efficiently on standard CPUs while achieving high precision. Validated on Gaussian mixtures and CIFAR-10 images, H-PID reveals a "weighted state" parameter as an order parameter in a dynamic phase transition, signaling early completion of the sampling process. This feature positions H-PID as a strong alternative to traditional methods sampling, such as simulated annealing, particularly for applications that demand analytical control, computational efficiency, and scalability. In this manuscript, we present a novel approach for sampling from a continuous multivariate probability distribution, which may either be explicitly known (up to a normalization factor) or represented via empirical samples. Our method constructs a time-dependent bridge from a delta function centered at the origin of the state space at t = 0, optimally transforming it into the target distribution at t = 1. We formulate this as a Stochastic Optimal Control problem of the Path Integral Control type, with a cost function comprising (in its basic form) a quadratic control term

关键词： Cost functions

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Bibliometric Analysis: Research Trends in Leaf Image Segmentation and Classification

Bibliometric Analysis: Research Trends in Leaf Image Segment...

引用

2024 International Conference on Artificial Intelligence and Mechatronics System, AIMS 2024

作者： Agustini, Eka Puji Gernowo, Rahmad Kurnianingsih Wibowo, Adi Warsito, Budi Doctoral Program of Information System School of Postgraduated Studies Diponegoro University Semarang Indonesia Doctoral Program of Information System Diponegoro University Semarang Indonesia Master of Applied Science Program Polytechnic Semarang Indonesia Diponegoro University Faculty of Science and Mathematics Department of Informatics Semarang Indonesia Faculty of Science and Mathematics Diponegoro Universitty Department of Statistics Semarang Indonesia

ISBN: (纸本)9798350350524

Exploring various phenomena and issues related to leaf images is paramount, particularly in segmentation and classification of such images. This study employs bibliometric analysis to delve into two overarching themes: The trends in publication and the evolution of publications, along with a keyword-based analysis. The research methodology unfolds in two stages: (1) data collection and (2) analysis. The dataset comprises 1,248 articles sourced from the Scopus database, covering the period from 1988 to 2023. The research findings unveil a noteworthy surge in publication trends, peaking at 231 documents in 2023. An in-depth examination of journal names demonstrates that studies on the segmentation and classification of leaf images are predominantly featured in computer science journals, exemplified by the publication of 589 documents. Furthermore, an analysis of frequently used keywords highlights 'Extraction' as the predominant term, employed a total of 364 times. This underscores that the research focus on leaf image segmentation and classification presents ample opportunities for researchers to delve more profoundly into the subject. © 2024 IEEE.

关键词： Image segmentation

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Correlations in interacting electron liquids: Many-body statistics and hyperuniformity

引用

Physical Review B 2024年第10期110卷 104201页

作者： Haina Wang Rhine Samajdar Salvatore Torquato Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Materials Institute Program in Applied and Computational Mathematics

Disordered hyperuniform many-body systems are exotic states of matter with novel optical, transport, and mechanical properties. These systems are characterized by an anomalous suppression of large-scale density fluctuations compared to ordinary liquids. The structure factor of disordered hyperuniform systems often obeys the scaling relation S(k)∼Bkα with B,α>0 in the limit k→0. Ground states of d-dimensional free fermionic gases, which are fundamental models for many metals and semiconductors, are key examples of quantum disordered hyperuniform states with important connections to random matrix theory. However, the effects of electron-electron interactions as well as the polarization of the electron liquid on hyperuniformity have not been explored thus far. In this paper, we systematically address these questions by deriving the analytical small-k behaviors (and, associated, α and B) of the total and spin-resolved structure factors of quasi-one-dimensional, two-dimensional, and three-dimensional electron liquids for varying polarizations and interaction parameters. We validate that these equilibrium disordered ground states are hyperuniform, as dictated by the fluctuation-compressibility relation. Interestingly, free fermions, partially polarized interacting fermions, and fully polarized interacting fermions are characterized by different values of the small-k scaling exponent α and coefficient B. In particular, partially polarized fermionic liquids exhibit a unique form of multihyperuniformity, in which the net configuration exhibits a stronger form of hyperuniformity (i.e., larger α) than each individual spin component. The detailed theoretical analysis of such small-k behaviors enables the construction of corresponding equilibrium classical systems under effective one- and two-body interactions that mimic the pair statistics of quantum electron liquids. Our paper thus reveals that highly unusual hyperuniform and multihyperuniform states can be achieved in simple

关键词： Electronic structure Quantum many-body systems Two-dimensional electron gas

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Essentially Commuting with a Unitary

arXiv

引用

arXiv 2025年

作者： Chung, Jui-Hui Shapiro, Jacob Program in Applied and Computational Mathematics Princeton University United States Department of Mathematics Princeton University United States

Let R be a unitary operator whose spectrum is the circle. We show that the set of unitaries U which essentially commute with R (i.e., [U, R] ≡ UR − RU is compact) is path-connected. Moreover, we also calculate the set of path-connected components of the orthogonal projections which essentially commute with R and obey a non-triviality condition, and prove it is bijective with Z. Copyright © 2025, The Authors. All rights reserved.

关键词：

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